User blog:Holomanga/Building Megastructures
The importance of a cause area, as ranked by 80,000 hours, my favourite effective altruist organisation, is calculated by80,000 Hours; How to compare different global problems in terms of impact :scale × neglectedness × solvability This expression actually breaks down to :good done / % of problem solved × % of problem solved / % increase in resources × % increase in resources / extra person or dollar Which cancels out to :good done / extra person or dollar Cost efficiency! Now, for engineering megastructures, the extra person or dollar is hard to judge (space empires don't use dollars, and "person" is fuzzy), so it should be converted into the truly universal currency: mass and energy I'm assuming that the civilisation isn't constrained by full time workers - possibly due to general purpose AI making that easy to deal with - or by active supporters - possibly due to coordination problems being resolved for advanced civilisations. The relative value of mass and energy depends on the civilisation: advanced civilisations can burn their resources to generate energy more effectively, so mass becomes more valuable. The mass and energy available to civilisations of various types is listed by Freitas asFreitas, Robert; Xenology 19.2 Extraterrrestrial Habitat Engineering: So, for a planetbound civilisation, one kilogram is worth about 108 J, and for a spacefaring civilisation, one kilogram is worth around 1015 J. The fundamental limit is an exchange rate of 1017 J·kg-1, the energy that a piece of matter has through E=mc2.Radiation has more energy than this still, theoretically having infinite energy per unit mass for electromagnetic radiation, though a sufficiently small amount of the energy in the universe is radiation that it can be neglected. Also, in the ultrarelativistic limit, energy and mass aren't sharply distinguished; radiation gravitates as if it has mass, for example. Our type 0.7 civilisation has a GDP of about 106.5 dollars per second for an energy output of 1013 joules per second, for an exchange rate of 106.5 joules per dollar (~3 MJ·$-1, ~1 kWh·$-1). This is about ten times higher than actual electricity prices, which suggests that each dollar spent on electricity is doing ten dollars worth of production. Pretty good investment! Applying our ratio of 108 means that this is worth 10-1.5 kg (~30 g). This is about twice as good as the economic output you'd get from perfectly burning a fossil fuel, though I guess if you average over fossil fuels and uranium and deuterium and solar power and stuff it might be in the ballpark (and also not forgetting that the ratio tracks technology, so our Type 0.7 civilisation might be doing a bit worse on the energy efficiency front). I think coal mining and energy collection are double counted in GDP, so when giving actual economic values I'll divide the prices, using 106 J·$-1 as the raw energy price. For Megastructures For a megastructure, we could use the available surface area as a good proxy for good done. This is because most of what you can do with a megastructure - habitable area, computations (due to heat dissipation considerations), energ collection - is proportional to the surface area. I'm not distinguishing things like internal surface area, exposed surface area, and so on, because that depends on the specific megastructure geometry and reasonable megastructures are thin anyway. The Costs of Our Megastructures Interestingly, the energy requirements are much smaller than the mass requirements in value (the only exception being the Cole Planetoid); an advanced civilisation looking to build a megastructure will find itself constrained much more by the mass requirements than the energy ones. It takes some very inefficient power plants before you're burning enough mass for it to be a worry for advanced civilisations, it seems. The costs per area are adjusted based on the productivity of the civilisation: values for Type 2, 3 and 4 civilisations are divided by 107, to account for the more efficient use of resources. Conclusions The best habitable megastructure is the humble O'Neill cylinder, with its small costs of just ¤105 per square metre, and the worst is the Alderson disk, at a costly ¤1011 per square metre. The costs for many very large megastructures come to around ¤1010 per square metre. Unless it's useful (say, for large-scale computation or energy gathering or something), civilisations will preferentially build small megastructures; this is expected, due to the square-cube law. Large megastructures are still more efficient than the raw square-cube law would suggest; this would predict the log of the cost being half the log of the area. A plot is shown of the actual line of best fit, versus that expected by the square cub law. The explanation is that large megastructures can be much thinner compared to their size than small megastructures - a solid dyson sphere can be characterised as a ping pong ball surrounding a star. Footnotes References Category:Blog posts